Question

Let X equal the butterfat production (in pounds) of a Holstein cow during the 305-day milking period following the birth of a calf. Assume that the distribution of X is N(μ,1402). To test the null hypothesis H0: μ = 715 against the alternative hypothesis H1: μ < 715, let the critical region be defined by C = {x : x ≤ 668.94}, where x is the sample mean of n = 25 butterfat weights from 25 cows selected at random.
(a) Find the power function K(μ) for this test.
(b) What is the significance level of the test?
(c) What are the values of K(668.94) and K(622.88)?
(d) Sketch a graph of the power function.
(e) What conclusion do you draw from the following 25 observations of X?